Playing the devil's advocate for the Diablo loot type: randomly generated items will theoritically never get old; each one will be a different item than the other. The same can't be said about your M60 example. After you find one, what will you'll find next? A m249. Ok, and after that? A gatling gun? And after that? and so on. You'll have variety for variety's sake.
It is certainly a difficult system to tweak.
I was thinking of Fallout New Vegas. Hidden in a corner of the map you could find a
special minigun in bottom of a crater, that had its own model. Every weapon had its unique type. They were a blast to find and to have. This, could be the case here. Say, "Maria", a special 9 mm pistol with a customized grip (cough cough) would be found in the cellar of house x in the map, be it Navezgane or RGW.
Another case comes to mind. Team Fortress 2 has different versions of each weapon. Interestingly, none is better than the other.
The Brass Beast for example, is a variation of the Minigun; it hinders your movement while firing even more but deals more damage.
I think this sort of "creative precision" could be nice to see and would complement what you have in mind.